Statistics II for IB: Time Series Analysis

A statistical method used to smooth out data by averaging values over a specified number of periods.

A type of moving average where more recent observations are given greater weight in the calculation. This type of smoothing is considered to be more responsive to changes in the data than a simple moving average.

The correlation between a time series and itself at different points in time. It measures how strongly a value at a specific point in time is related to values at previous or future points in time.

A type of statistical model used to forecast future values in a time series based on past values. This model assumes that the future values are influenced by past values.

A line chart used to visualize data over time. It helps identify trends and patterns in the data.

A type of trend in a time series where the data tends to increase over time.

A type of trend in a time series where the data tends to decrease over time.

A type of trend in a time series where the data oscillates around a constant average.

A moving average that is calculated by taking the average of a specific number of data points, then moving the window of data points forward by one, and repeating the process. This creates smoother trends and reduces the impact of fluctuations in the raw data.

A parameter used in exponential smoothing that controls the influence of past data on the current forecast. A higher alpha value means a larger weight is given to recent data, making the forecast more sensitive to recent changes, while a lower alpha value emphasizes past data.

A statistical test used to detect autocorrelation in a time series. The Durbin-Watson statistic measures the correlation between consecutive residuals of a regression model.

The Durbin-Watson (DW) test is a statistical test used to detect autocorrelation, which is the presence of a relationship between error terms in a time series model. It assesses whether the residuals are independent or correlated, suggesting that the model's assumptions are violated. A DW value near 2 indicates no autocorrelation, while values close to 0 or 4 suggest positive or negative autocorrelation, respectively. The test typically provides a critical value range, often between 1.5 and 2.5, which helps determine the significant level of autocorrelation based on the calculated DW statistic.

The Durbin-Watson statistic is a numerical value calculated from the residuals of a regression analysis, ranging between 0 and 4. It measures the degree of autocorrelation in the time series data. A value close to 2 suggests no autocorrelation, while values closer to 0 or 4 indicate positive or negative autocorrelation, respectively. The statistic provides insight into the independence of error terms, which is crucial for validating statistical assumptions in time series models.

The Autoregressive (AR) process is a statistical model that uses past values of a time series to predict its future values. It assumes that a variable's current value is dependent on its past values, creating a relationship between them. The AR(1) process, in particular, considers only the previous period's value in predicting the current value. This process is often used in time series analysis to model the relationship between a variable's past and future values.

The Autocorrelation Function (ACF) measures the correlation between the values of a time series and its lagged (past) values. It visually represents how strongly values at different time points are related. The plot typically displays the correlation coefficients for various lags, indicating the strength of the relationship at different time intervals. The ACF helps identify the presence of patterns and trends in time series data, providing insights into the dependency structure of the data.

The Partial Autocorrelation Function (PACF) measures the correlation between a time series and its lagged values, removing the influence of the intervening values. Unlike the ACF, the PACF focuses on the direct relationship between a value and its lagged value, eliminating the effect of other intervening values in the time series. It helps identify the direct dependence of a value on its lagged values, providing insights into the direct relationship between values at different time lags.

The correlogram plot is a graphical representation of the autocorrelation function (ACF) and partial autocorrelation function (PACF) of a time series. It visually displays the correlation coefficients for various lags, providing insights into the dependence structure of the data. The correlogram plot helps identify patterns and trends in time series data, indicating the presence of autocorrelation and the appropriate model structure for analysis.

Time series analysis focuses on understanding and predicting data that is measured over time. It involves modeling and interpreting the relationships between values collected over different periods. Time series analysis is essential for forecasting future trends, understanding seasonal patterns, identifying anomalies, and uncovering inherent relationships within the data, leading to better decision-making based on time-dependent information.